非相似图导向IFS的分形维数估计
A fractal dimension estimate for a graph-directed IFS of non-similarities
摘要：
设一个图定向迭代函数系由映射f_e组成，其上估计为d（f_e（x），f_e（y））<= r_e d（x，y）.则IFS的吸引子K_v的分维由与具有比率r_e的Mauldin-Williams图相关联的维数上界。设映射f_e也有形式为d（f_e（x），f_e（y））>= r '_e d（x，y）的下估计，且IFS也满足强开集条件.则IFS的吸引子K_v的分维由与具有比率r '_e的Mauldin-Williams图相关联的维数下界。当r_e = r '_e时，则映射是相似的，这就简化为Mauldin & Williams在这种情况下的维数计算。
英文摘要：
Suppose a graph-directed iterated function system consists of maps f_e with upper estimates of the form d(f_e(x),f_e(y)) <= r_e d(x,y). Then the fractal dimension of the attractor K_v of the IFS is bounded above by the dimension associated to the Mauldin--Williams graph with ratios r_e. Suppose the maps f_e also have lower estimates of the form d(f_e(x),f_e(y)) >= r'_e d(x,y) and that the IFS also satisfies the strong open set condition. Then the fractal dimension of the attractor K_v of the IFS is bounded below by the dimension associated to the Mauldin--Williams graph with ratios r'_e. When r_e = r'_e, then the maps are similarities and this reduces to the dimension computation of Mauldin & Williams for that case.
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